Gauss Law

 Today we are going to deal about the topic electric flux and Gauss law.

Electric Flux:

Electric flux is defined as the number of electric field lines passing normally through a given area per unit time. For example if we consider 100 N/C electric field passing normally through 20 m² area. Then the electric flux through the given surface area is 2000 N m²/C.

Generalized formula:

Electric Flux ( ϕ ) = Electric field * Area * cos T, 

where T is the angle between the electric field vector 

and the area vector

Gauss Law:

According to the Gauss law, the total flux linked with a closed surface is 1/ε₀ times the charge enclosed by the closed surface.

ϕ = q _{enclosed by the Gaussian surface} / ε₀

Question for practice:

Q1. Find the net flux through the curved surface area of the cone:

     

Ans: the net flux through the total Gaussian surface is q/ε₀. Since flux is not a vector quantity, we can write net flux = flux through the hemisphere (ϕ 1) + flux through the curved surface of cone (ϕ 2).

So

ϕ _net = ϕ ₁ +ϕ ₂

ϕ ₂= ϕ _net - ϕ ₁

ϕ ₂ = q/ε₀ - q/ 2ε₀

= q/2ε₀